Ankara has offered to deploy troops at Afghanistan's Kabul airport after NATO fully withdraws and has been in talks with the United States for several weeks.
The incident comes a day after the Afghanistan government said it repelled a Taliban assault on the key border crossing with Pakistan amid the militants' sweeping advance.
Thousands of Afghans have left behind escalating violence to seek shelter elsewhere in the country amid ongoing withdrawal of US and NATO troops.
The seizure of Nerkh district comes amid intensifying violence following an announcement by the group of a three-day ceasefire in Afghanistan for the Muslim religious holiday of Eid, starting this week.
Violence in the country has been rising sharply in recent weeks after the United States announced it would withdraw troops by September 11.
President Ashraf Ghani offers a share in power to Taliban, provided the militant group "gives up the war" as Afghanistan celebrates Victory Day to mark Mujahideen's overthrowing of Soviet-backed Kabul regime in 1992.
Kabul and several other provinces of Afghanistan have been rocked by deadly violence, including bombings, rocket attacks and targeted killings in recent months.
The group has modified its aims to try and pose a new challenge to the Pakistani state which has so far succeeded in pushing it underground.
The estranged Pakistani Taliban leaders shunned their differences in light of Daesh's growing foothold and joint anti-terror operations by the US, Pakistan and Afghanistan.
Taliban orders fighters to observe three-day ceasefire in Afghanistan for Eid al Adha holiday, starting on Friday, as President Ghani says peace talks with insurgents could begin in seven days.
They were travelling in a car and stopped at a Taliban checkpoint on the road, Paktia governor spokesman Abdullah Hasrat said. The Taliban has long targeted the judiciary in retaliation for harsh sentences given to their fighters.
As civilians prepare to head to the polls on Saturday, few expect the presidential election will have much effect in bringing peace to the war-torn country.
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